DM41X 41z Module

• assign the complex keyboard Z to USER menu on key Σ+
  • SHIFT ASN ALPHA Z K B R D ALPHA Σ+
  • Enter USER mode with USR key
  • The Σ+ now activates a complex number function when it's pressed - for one operation only

To simplify use it's possible change the keyboard to the complex keyboard, and remove the need to trigger every command with Z

Enable the keyboard with ZK?YN and answer Y.

Put ZK?YN on the CST custom user menu for quick access!

Now the USER keyboard is re-mapped to match the overlay and things are much easier. To use normal functions simply press USR to temporarily switch off the complex keyboard. Press USR to switch back to complex mode. To leave complex mode completely and return USER keyboard to normal re-run ZK?YN and answer N

To enter a complex number in this mode :

2 + 3i

2 ENTER 3 ENTER

To add 2 + 3i + 10 - 4i

2 ENTER 3 ENTER

10 ENTER 4 CHS ENTER

+

Result:

12 - j 1

The alternative “permanent Z-Keyboard” method is less cumbersome and more intuitive.

e.g. POLAR mode

Enter a complex number in rectangular mode and then switch to POLAR mode

50 ENTER 23 ENTER

ZZ6

55.04 ∠ 24.70

All further entries will remain as POLAR

eg a new complex number in POLAR format

100 ∠ - 85

100 ENTER 85CHS ENTER

display :

100 ∠ - 85

Switch back to RECT mode

ZZ5

8.72 - 99.62

• Z = Σ+

• ↑IM/AG = Z XEQ
• ZREAL↑ = Z Z RCL
• ZIMAG↑ = Z Z XEQ
• ZINV = Z 1/X
• POLAR = Z Z R→P (i.e. 6)
• RECT = Z Z P→R (i.e. 5)
• ZCONJ = Z SHIFT CHS (complex conjugate)
• Z ^ X = Z EEX
• Z ^ 1/X = Z Z EEX

• Enter a complex number to the stack
  • 5 + j 20
    • 5 Z XEQ 2 0 ENTER
      • Z XEQ is ^IM/AG - set the imaginary part
• add a second number to the stack
  • 10 - j 32
    • 10 Z XEQ 3 2 CHS ENTER
• add the two numbers together
  • Z +
• 15 - j 12

This involves the complex inverse function Z 1/x

• Z1 = 50 + j 13 in parallel with Z2 = 23 - j 85
  • enter Z1 50 Z XEQ 13 ENTER and invert it Z 1/X
    • 0.02 - j 4.87E-3
  • enter Z2 23 Z XEQ 85 CHS ENTER and invert it Z 1/X
    • 2.97E-3 + j0.01
  • add them together Z +
    • 0.02 +j0.01 and invert Z 1/X
      • 42.72 - j 11.99

50 ENTER 13 ENTER

1/x

23 ENTER 85CHS ENTER

1/x

+

1/x

Result :

42.72 - j 11.99

• Z = 50 - j 23
• in polar form…
  • enter Z as usual
  • convert to Polar format
    • Z Z 6 ( 6 is R→P but needs two presses of Z to activate it)
    • 55.04 ∠ -24.70
  • convert back to Rectangular operation
    • Z Z 5
    • 50 - j 23

• To enter 5 ∠ 53.13 directly
  • switch to Polar format Z Z 6
  • enter Mag / Angle:
    • 5 Z XEQ 53.13 ENTER
    • display : 5 ∠ 53.13
• convert to Rect
  • Z Z 5
    • display : 3.00 + j 4.00

• key Imaginary part first & press normal ENTER
• key real part (and no ENTER)
• do complex enter (Z ENTER) or another complex function (e.g. Z +) (be careful with the stack lift or it gets confusing)
• e.g. 52 + j 36
  • 36 ENTER 52 Z ENTER
  • 52 + j 36 is now in Stack
• enter second number
• e.g. 23 - j 15
  • 15 CHS ENTER 23 (don't Z ENTER this…!!)
• to add them together use Z + now (instead of Z ENTER)
• result : 75 + j 21

• pressing Z ENTER after the second number (instead of the required complex function) will give you

doing a Z + now will add the second number to itself and the result will be 46 - j 30

This is normal RPN stack behaviour, but is confusing when you're building complex numbers.

The natural entry mode is much better

1. you enter the real and imaginary parts in the order you expect them
2. the stack operation is less obscure.
3. It just seems more intuitive.

Page created Wed May 25 15:14:29 2022 by John Pumford-Green

Page last updated: 05/09/24 11:38 BST